Kernelized linear principal component discriminant analysis.

Area of Science:

• Machine Learning
• Data Science
• Pattern Recognition

Background:

• Existing discriminant analysis methods often use disjointed multi-stage approaches (e.g., PCA+LDA, KPCA+GDA).
• This fragmentation can lead to suboptimal performance by treating feature extraction and class discrimination separately.

Purpose of the Study:

• To introduce Kernelized Linear Principal Component Discriminant Analysis (KLPCDA), a unified framework for discriminant analysis.
• To integrate feature extraction and class discrimination into a single optimization model within the Reproducing Kernel Hilbert Space (RKHS).
• To provide a flexible and adaptable discriminant analysis method that outperforms existing approaches.

Main Methods:

• Developed KLPCDA, a joint optimization model in RKHS that fuses variance preservation, between-class separation, and within-class compactness.
• Formulated seven KLPCDA variants with tunable fusion coefficients for flexible control over objective criteria.
• Implemented a systematic parameter optimization strategy, including kernel selection, dimensionality tuning, and fusion balancing.

Main Results:

• KLPCDA demonstrated consistent superiority over benchmark methods and CNNs in small-sample-size (SSS) settings across diverse datasets (image, tabular, signal).
• Achieved higher recognition accuracy and efficiency in SSS scenarios compared to existing methods.
• Maintained competitive computational complexity and storage efficiency in large-scale settings.

Conclusions:

• KLPCDA offers a robust and adaptable solution for discriminant analysis, effectively unifying feature extraction and class discrimination.
• The framework shows significant advantages in both small-sample-size and large-scale machine learning applications.
• Provides a foundation for future research in advanced discriminant analysis techniques.